The CIMA P2 Limiting Factor Analysis Mistake That Costs Marks

When CIMA P2 gives you a single scarce resource and asks for the optimal production plan, there is one number examiners are specifically checking, and it is not contribution per unit. It is contribution per unit of the scarce resource. Rank by the wrong measure and every mark that depends on the resulting production plan is at risk, even if every individual contribution calculation was correct.

Why ranking by contribution per unit fails

Contribution per unit tells you how profitable a single unit of a product is. It says nothing about how much of the scarce resource that unit consumes to be made. When machine hours, labour hours, or a key raw material are limited and every product competes for the same pool of that resource, the business should prioritise whichever product generates the most contribution from each hour or kilogram of the constrained input, not whichever product happens to look best per unit sold. A product with a high contribution per unit but a heavy appetite for the scarce resource can easily generate less total profit than a lower-margin product that uses the scarce resource sparingly.

This is limiting factor analysis, sometimes called key factor analysis, and it is a recurring theme in CIMA P2. The mechanics are not difficult once you have the method fixed, but under exam pressure it is very easy to default to ranking by the more familiar contribution-per-unit figure instead, especially when a question presents several products with similar-looking numbers.

The correct method: contribution per unit of scarce resource

The standard approach follows four steps:

1. Calculate contribution per unit for each product (selling price less variable cost per unit).
2. Identify how much of the scarce resource each unit of each product consumes.
3. Divide contribution per unit by the resource consumed per unit to get contribution per unit of scarce resource.
4. Rank products from highest to lowest contribution per unit of scarce resource, and allocate the available scarce resource to the top-ranked product first, up to its maximum demand, before moving to the next product, until the resource is exhausted.

This produces the production plan that maximises total contribution given the constraint. Any other ranking basis, including contribution per unit alone, will generally produce a lower total contribution once the scarce resource limit actually bites.

Worked example: three products, one binding constraint

A manufacturer makes three products, A, B and C, all of which pass through the same machine. Machine hours are the only binding constraint this period, with 2,500 hours available. The figures are:

On contribution per unit alone, B looks like the star product at $50 per unit, with A second at $30 and C trailing at $20. That ranking is the trap. Dividing contribution per unit by machine hours per unit gives the figure that actually matters:

C, the product that looked weakest per unit, is actually the most efficient use of the scarce machine hours, and B, the apparent star, is the least efficient. This reversal is exactly what CIMA P2 questions are built to test.

Building the optimal production plan

Allocate the 2,500 available hours in rank order, filling each product's maximum demand before moving down the ranking:

• C first: full demand of 800 units uses 800 hours (800 × 1). Hours remaining: 2,500 − 800 = 1,700.
• A second: full demand of 500 units uses 1,000 hours (500 × 2). Hours remaining: 1,700 − 1,000 = 700.
• B last: only 700 hours remain, and each unit of B needs 5 hours, so 700 ÷ 5 = 140 units of B can be made, against a maximum demand of 300. B production is rationed to 140 units, using all remaining hours.

Total contribution under the correct plan: (800 × $20) + (500 × $30) + (140 × $50) = $16,000 + $15,000 + $7,000 = $38,000, with all 2,500 machine hours fully used.

What the wrong ranking would have produced

Now compare the plan a candidate gets by ranking on contribution per unit instead, making B first, then A, then C:

• B first: full demand of 300 units uses 1,500 hours. Hours remaining: 2,500 − 1,500 = 1,000.
• A second: full demand of 500 units uses exactly 1,000 hours. Hours remaining: 0.
• C last: no hours remain, so zero units of C are made, despite demand for 800 units.

Total contribution under this wrong plan: (300 × $50) + (500 × $30) + (0 × $20) = $15,000 + $15,000 + $0 = $30,000. That is $8,000 less than the correct plan, purely because the ranking basis was wrong. On an exam, this is not a rounding error; it is the difference between a full-marks answer and one that loses every mark dependent on the production plan, including any follow-on profit or decision-making calculation built on top of it.

The related trap: does a make-or-buy option change the ranking?

A second, closely related trap in CIMA P2 questions is stopping at the ranking table without checking whether a make-or-buy option exists. If a product can be bought in from a subcontractor rather than made in-house, buying it in frees up scarce machine hours that can be redirected to a more efficient product, and that can be worth doing even for a product that already ranked reasonably well.

Take product A from the example above. Suppose a subcontractor can supply finished units of A for $52 each, while Learnsignal's manufacturer would otherwise make it in-house at a variable cost that produces the $30 contribution shown (implying a variable cost of roughly $40 against a $70 selling price, for illustration). Buying in one unit of A instead of making it costs an extra $12 over making it (the $52 buy-in price less the $40 saved variable cost). But it also frees 2 machine hours. Those 2 hours, redirected to the next-most-constrained product still being rationed — B, at $50 ÷ 5 = $10 per hour — generate 2 × $10 = $20 of extra contribution. Since the $20 benefit from redeploying the freed hours exceeds the $12 extra cost of buying A in, it is worth buying in some units of A and using the freed capacity to make more B, even though A ranked ahead of B in the original table.

The rule to apply in the exam: never assume the initial contribution-per-scarce-resource ranking is the final answer once a make-or-buy option is mentioned in the question. Recalculate the marginal benefit of freeing the scarce resource against the extra cost of buying in, for any product where an external supply option is offered, before finalising the production plan.

Exam technique summary

• Never rank products on contribution per unit alone when a single resource is limiting production.
• Always divide contribution per unit by the amount of scarce resource each unit consumes, then rank on that figure.
• Allocate the scarce resource to the highest-ranked product first, up to its maximum demand, before moving down the list.
• Where a make-or-buy option is offered, check whether buying in a product frees enough scarce resource to justify its extra cost, and be ready to revise the plan.
• State your ranking table explicitly in the answer; markers are checking the method, not just the final profit figure.

Limiting factor analysis sits alongside other short-run decision-making techniques on the syllabus, including activity-based costing vs absorption costing, where a similar habit of reaching for the more familiar method instead of the one the scenario actually calls for costs candidates marks. For the full syllabus context this topic sits within, the CIMA P2 Advanced Management Accounting materials cover limiting factor analysis alongside the other short-term decision-making techniques examined at this level.

Once the four-step method is automatic, limiting factor questions become one of the more reliable mark sources on the paper, precisely because the calculation itself is short. The marks are lost or won on choosing the right basis for the ranking, not on the arithmetic.